Lattices and Codes
A Course Partially Based on Lectures by Friedrich Hirzebruch
3rd Edition
Published on 18. September 2012
XVI, 167 pages
978-3-658-00360-9 (ISBN)
Description
The purpose of coding theory is the design of efficient systems for the transmission of information. The mathematical treatment leads to certain finite structures: the error-correcting codes. Surprisingly problems which are interesting for the design of codes turn out to be closely related to problems studied partly earlier and independently in pure mathematics. In this book, examples of such connections are presented. The relation between lattices studied in number theory and geometry and error-correcting codes is discussed. The book provides at the same time an introduction to the theory of integral lattices and modular forms and to coding theory.
In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated.
In the 3rd edition, again numerous corrections and improvements have been made and the text has been updated.
Reviews / Votes
From the reviews of the third edition:
"In the book under review, Ebeling explores the mathematical theory of lattices and the ways that it is used by coding theorists. . I very much enjoyed reading Ebeling's book. . This book contains some exciting mathematics, and I would recommend it to a graduate student or faculty member looking to learn about the field." (Darren Glass, MAA Reviews, April, 2013)
More details
Series
Edition
3rd rev. ed. 2013
Language
English
Place of publication
Wiesbaden
Germany
Publishing group
Springer Fachmedien Wiesbaden GmbH
Target group
Primary & secondary/elementary & high school
Illustrations
XVI, 167 p. 50 illus.
File size
1,35 MB
ISBN-13
978-3-658-00360-9 (9783658003609)
DOI
10.1007/978-3-658-00360-9
Schweitzer Classification
Other editions
Additional editions
Book
09/2012
3rd Edition
Springer Spektrum
€69.54
Shipment within 10-15 days
Person
Prof. Dr. Wolfgang Ebeling, Institute of Algebraic Geometry, Leibniz Universität Hannover, Germany
Fields of research: Algebraic Geometry, Differential Topology, Singularities
Content
Lattices and Codes.- Theta Functions and Weight Enumerators.- Even Unimodular Lattices.- The Leech Lattice.- Lattices over Integers of Number Fields and Self-Dual Codes.
